Title: Optimal detection of sparse principal components in high dimension
| Speaker: | Steve Vavasis |
| Affiliation: | University of Waterloo |
| Room: | MC 5417 |
Abstract:
I will present the paper with this title by Berthet and Rigollet (Ann. Stat., 41 (2013) 1780-1815, https://projecteuclid.org/download/pdfview_1/euclid.aos/1378386239). Their abstract is as follows: "We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on simulated datasets. Moreover, using polynomial time reductions from theoretical computer science, we bring significant evidence that our results cannot be improved, thus revealing an inherent trade off between statistical and computational performance." I will present their problem, sparse eigenvalue statistic, convex relaxation, and, time permitting, the polynomial-time reduction.